Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.28 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.29 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 11.4203i | 1.63148i | 0.578420 | + | 0.815739i | \(0.303669\pi\) | ||||
−0.578420 | + | 0.815739i | \(0.696331\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | 13.8723i | 1.26112i | 0.776141 | + | 0.630559i | \(0.217175\pi\) | ||||
−0.776141 | + | 0.630559i | \(0.782825\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | −2.98777 | −0.229829 | −0.114914 | − | 0.993375i | \(-0.536659\pi\) | ||||
−0.114914 | + | 0.993375i | \(0.536659\pi\) | |||||||
\(14\) | 16.1508i | 1.15363i | ||||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 15.3412i | 0.902426i | 0.892416 | + | 0.451213i | \(0.149009\pi\) | ||||
−0.892416 | + | 0.451213i | \(0.850991\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | − | 2.52942i | − | 0.133127i | −0.997782 | − | 0.0665636i | \(-0.978796\pi\) | ||
0.997782 | − | 0.0665636i | \(-0.0212035\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 19.7806i | 0.941934i | ||||||||
\(22\) | 19.6184i | 0.891746i | ||||||||
\(23\) | −20.9247 | − | 9.54768i | −0.909768 | − | 0.415117i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −4.22535 | −0.162513 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 22.8407i | 0.815739i | ||||||||
\(29\) | 11.6231 | 0.400798 | 0.200399 | − | 0.979714i | \(-0.435776\pi\) | ||||
0.200399 | + | 0.979714i | \(0.435776\pi\) | |||||||
\(30\) | − | 5.47723i | − | 0.182574i | ||||||
\(31\) | 2.71207 | 0.0874861 | 0.0437431 | − | 0.999043i | \(-0.486072\pi\) | ||||
0.0437431 | + | 0.999043i | \(0.486072\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 24.0275i | 0.728107i | ||||||||
\(34\) | 21.6958i | 0.638112i | ||||||||
\(35\) | 25.5367 | 0.729619 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 31.7707i | 0.858668i | 0.903146 | + | 0.429334i | \(0.141252\pi\) | ||||
−0.903146 | + | 0.429334i | \(0.858748\pi\) | |||||||
\(38\) | − | 3.57714i | − | 0.0941352i | ||||||
\(39\) | −5.17497 | −0.132692 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | 36.3226 | 0.885917 | 0.442959 | − | 0.896542i | \(-0.353929\pi\) | ||||
0.442959 | + | 0.896542i | \(0.353929\pi\) | |||||||
\(42\) | 27.9740i | 0.666048i | ||||||||
\(43\) | − | 19.9718i | − | 0.464461i | −0.972661 | − | 0.232231i | \(-0.925398\pi\) | ||
0.972661 | − | 0.232231i | \(-0.0746024\pi\) | |||||||
\(44\) | 27.7446i | 0.630559i | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | −29.5920 | − | 13.5025i | −0.643303 | − | 0.293532i | ||||
\(47\) | 52.2318 | 1.11131 | 0.555657 | − | 0.831411i | \(-0.312467\pi\) | ||||
0.555657 | + | 0.831411i | \(0.312467\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −81.4243 | −1.66172 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 26.5718i | 0.521016i | ||||||||
\(52\) | −5.97554 | −0.114914 | ||||||||
\(53\) | − | 59.4952i | − | 1.12255i | −0.827629 | − | 0.561275i | \(-0.810311\pi\) | ||
0.827629 | − | 0.561275i | \(-0.189689\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | 31.0194 | 0.563990 | ||||||||
\(56\) | 32.3016i | 0.576815i | ||||||||
\(57\) | − | 4.38108i | − | 0.0768611i | ||||||
\(58\) | 16.4376 | 0.283407 | ||||||||
\(59\) | 81.6065 | 1.38316 | 0.691581 | − | 0.722299i | \(-0.256915\pi\) | ||||
0.691581 | + | 0.722299i | \(0.256915\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | 42.2136i | 0.692026i | 0.938230 | + | 0.346013i | \(0.112465\pi\) | ||||
−0.938230 | + | 0.346013i | \(0.887535\pi\) | |||||||
\(62\) | 3.83545 | 0.0618620 | ||||||||
\(63\) | 34.2610i | 0.543826i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 6.68086i | 0.102782i | ||||||||
\(66\) | 33.9801i | 0.514850i | ||||||||
\(67\) | − | 58.5139i | − | 0.873342i | −0.899621 | − | 0.436671i | \(-0.856157\pi\) | ||
0.899621 | − | 0.436671i | \(-0.143843\pi\) | |||||||
\(68\) | 30.6825i | 0.451213i | ||||||||
\(69\) | −36.2426 | − | 16.5371i | −0.525255 | − | 0.239668i | ||||
\(70\) | 36.1143 | 0.515919 | ||||||||
\(71\) | 100.588 | 1.41673 | 0.708367 | − | 0.705844i | \(-0.249432\pi\) | ||||
0.708367 | + | 0.705844i | \(0.249432\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | −16.7595 | −0.229582 | −0.114791 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114791 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(74\) | 44.9306i | 0.607170i | ||||||||
\(75\) | −8.66025 | −0.115470 | ||||||||
\(76\) | − | 5.05884i | − | 0.0665636i | ||||||
\(77\) | −158.427 | −2.05749 | ||||||||
\(78\) | −7.31852 | −0.0938271 | ||||||||
\(79\) | − | 60.6495i | − | 0.767715i | −0.923392 | − | 0.383858i | \(-0.874595\pi\) | ||
0.923392 | − | 0.383858i | \(-0.125405\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 51.3679 | 0.626438 | ||||||||
\(83\) | − | 44.1530i | − | 0.531964i | −0.963978 | − | 0.265982i | \(-0.914304\pi\) | ||
0.963978 | − | 0.265982i | \(-0.0856962\pi\) | |||||||
\(84\) | 39.5612i | 0.470967i | ||||||||
\(85\) | 34.3041 | 0.403577 | ||||||||
\(86\) | − | 28.2444i | − | 0.328424i | ||||||
\(87\) | 20.1319 | 0.231401 | ||||||||
\(88\) | 39.2368i | 0.445873i | ||||||||
\(89\) | 106.245i | 1.19376i | 0.802330 | + | 0.596881i | \(0.203594\pi\) | ||||
−0.802330 | + | 0.596881i | \(0.796406\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | − | 34.1214i | − | 0.374960i | ||||||
\(92\) | −41.8493 | − | 19.0954i | −0.454884 | − | 0.207558i | ||||
\(93\) | 4.69744 | 0.0505101 | ||||||||
\(94\) | 73.8669 | 0.785818 | ||||||||
\(95\) | −5.65595 | −0.0595363 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | − | 37.9918i | − | 0.391668i | −0.980637 | − | 0.195834i | \(-0.937259\pi\) | ||
0.980637 | − | 0.195834i | \(-0.0627414\pi\) | |||||||
\(98\) | −115.151 | −1.17501 | ||||||||
\(99\) | 41.6169i | 0.420373i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −147.465 | −1.46005 | −0.730024 | − | 0.683422i | \(-0.760491\pi\) | ||||
−0.730024 | + | 0.683422i | \(0.760491\pi\) | |||||||
\(102\) | 37.5782i | 0.368414i | ||||||||
\(103\) | − | 74.8003i | − | 0.726217i | −0.931747 | − | 0.363108i | \(-0.881715\pi\) | ||
0.931747 | − | 0.363108i | \(-0.118285\pi\) | |||||||
\(104\) | −8.45069 | −0.0812567 | ||||||||
\(105\) | 44.2308 | 0.421246 | ||||||||
\(106\) | − | 84.1389i | − | 0.793763i | ||||||
\(107\) | − | 36.8895i | − | 0.344762i | −0.985030 | − | 0.172381i | \(-0.944854\pi\) | ||
0.985030 | − | 0.172381i | \(-0.0551460\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | − | 89.1884i | − | 0.818242i | −0.912480 | − | 0.409121i | \(-0.865835\pi\) | ||
0.912480 | − | 0.409121i | \(-0.134165\pi\) | |||||||
\(110\) | 43.8681 | 0.398801 | ||||||||
\(111\) | 55.0285i | 0.495752i | ||||||||
\(112\) | 45.6814i | 0.407869i | ||||||||
\(113\) | 39.7138i | 0.351450i | 0.984439 | + | 0.175725i | \(0.0562269\pi\) | ||||
−0.984439 | + | 0.175725i | \(0.943773\pi\) | |||||||
\(114\) | − | 6.19578i | − | 0.0543490i | ||||||
\(115\) | −21.3493 | + | 46.7890i | −0.185646 | + | 0.406861i | ||||
\(116\) | 23.2463 | 0.200399 | ||||||||
\(117\) | −8.96331 | −0.0766095 | ||||||||
\(118\) | 115.409 | 0.978043 | ||||||||
\(119\) | −175.202 | −1.47229 | ||||||||
\(120\) | − | 10.9545i | − | 0.0912871i | ||||||
\(121\) | −71.4409 | −0.590421 | ||||||||
\(122\) | 59.6990i | 0.489336i | ||||||||
\(123\) | 62.9126 | 0.511485 | ||||||||
\(124\) | 5.42414 | 0.0437431 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 48.4524i | 0.384543i | ||||||||
\(127\) | −130.656 | −1.02878 | −0.514392 | − | 0.857555i | \(-0.671982\pi\) | ||||
−0.514392 | + | 0.857555i | \(0.671982\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 34.5922i | − | 0.268157i | ||||||
\(130\) | 9.44816i | 0.0726782i | ||||||||
\(131\) | 2.98786 | 0.0228081 | 0.0114041 | − | 0.999935i | \(-0.496370\pi\) | ||||
0.0114041 | + | 0.999935i | \(0.496370\pi\) | |||||||
\(132\) | 48.0551i | 0.364054i | ||||||||
\(133\) | 28.8868 | 0.217194 | ||||||||
\(134\) | − | 82.7512i | − | 0.617546i | ||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | 43.3916i | 0.319056i | ||||||||
\(137\) | 120.177i | 0.877207i | 0.898681 | + | 0.438603i | \(0.144527\pi\) | ||||
−0.898681 | + | 0.438603i | \(0.855473\pi\) | |||||||
\(138\) | −51.2548 | − | 23.3869i | −0.371411 | − | 0.169471i | ||||
\(139\) | −127.272 | −0.915628 | −0.457814 | − | 0.889048i | \(-0.651367\pi\) | ||||
−0.457814 | + | 0.889048i | \(0.651367\pi\) | |||||||
\(140\) | 51.0733 | 0.364810 | ||||||||
\(141\) | 90.4681 | 0.641618 | ||||||||
\(142\) | 142.253 | 1.00178 | ||||||||
\(143\) | − | 41.4473i | − | 0.289841i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | − | 25.9901i | − | 0.179242i | ||||||
\(146\) | −23.7015 | −0.162339 | ||||||||
\(147\) | −141.031 | −0.959395 | ||||||||
\(148\) | 63.5414i | 0.429334i | ||||||||
\(149\) | 131.641i | 0.883494i | 0.897140 | + | 0.441747i | \(0.145641\pi\) | ||||
−0.897140 | + | 0.441747i | \(0.854359\pi\) | |||||||
\(150\) | −12.2474 | −0.0816497 | ||||||||
\(151\) | 149.135 | 0.987650 | 0.493825 | − | 0.869561i | \(-0.335598\pi\) | ||||
0.493825 | + | 0.869561i | \(0.335598\pi\) | |||||||
\(152\) | − | 7.15427i | − | 0.0470676i | ||||||
\(153\) | 46.0237i | 0.300809i | ||||||||
\(154\) | −224.049 | −1.45486 | ||||||||
\(155\) | − | 6.06437i | − | 0.0391250i | ||||||
\(156\) | −10.3499 | −0.0663458 | ||||||||
\(157\) | − | 228.188i | − | 1.45343i | −0.686941 | − | 0.726713i | \(-0.741047\pi\) | ||
0.686941 | − | 0.726713i | \(-0.258953\pi\) | |||||||
\(158\) | − | 85.7713i | − | 0.542857i | ||||||
\(159\) | − | 103.049i | − | 0.648105i | ||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | 109.038 | − | 238.967i | 0.677253 | − | 1.48427i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 260.536 | 1.59838 | 0.799191 | − | 0.601077i | \(-0.205261\pi\) | ||||
0.799191 | + | 0.601077i | \(0.205261\pi\) | |||||||
\(164\) | 72.6452 | 0.442959 | ||||||||
\(165\) | 53.7272 | 0.325620 | ||||||||
\(166\) | − | 62.4418i | − | 0.376155i | ||||||
\(167\) | −177.110 | −1.06054 | −0.530271 | − | 0.847828i | \(-0.677910\pi\) | ||||
−0.530271 | + | 0.847828i | \(0.677910\pi\) | |||||||
\(168\) | 55.9480i | 0.333024i | ||||||||
\(169\) | −160.073 | −0.947179 | ||||||||
\(170\) | 48.5133 | 0.285372 | ||||||||
\(171\) | − | 7.58825i | − | 0.0443758i | ||||||
\(172\) | − | 39.9437i | − | 0.232231i | ||||||
\(173\) | 7.60898 | 0.0439825 | 0.0219913 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219913 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(174\) | 28.4708 | 0.163625 | ||||||||
\(175\) | − | 57.1017i | − | 0.326296i | ||||||
\(176\) | 55.4892i | 0.315280i | ||||||||
\(177\) | 141.347 | 0.798568 | ||||||||
\(178\) | 150.253i | 0.844118i | ||||||||
\(179\) | 319.384 | 1.78427 | 0.892133 | − | 0.451772i | \(-0.149208\pi\) | ||||
0.892133 | + | 0.451772i | \(0.149208\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | − | 115.161i | − | 0.636248i | −0.948049 | − | 0.318124i | \(-0.896947\pi\) | ||
0.948049 | − | 0.318124i | \(-0.103053\pi\) | |||||||
\(182\) | − | 48.2549i | − | 0.265137i | ||||||
\(183\) | 73.1161i | 0.399541i | ||||||||
\(184\) | −59.1839 | − | 27.0049i | −0.321652 | − | 0.146766i | ||||
\(185\) | 71.0414 | 0.384008 | ||||||||
\(186\) | 6.64319 | 0.0357161 | ||||||||
\(187\) | −212.818 | −1.13807 | ||||||||
\(188\) | 104.464 | 0.555657 | ||||||||
\(189\) | 59.3419i | 0.313978i | ||||||||
\(190\) | −7.99872 | −0.0420985 | ||||||||
\(191\) | − | 104.681i | − | 0.548068i | −0.961720 | − | 0.274034i | \(-0.911642\pi\) | ||
0.961720 | − | 0.274034i | \(-0.0883581\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 58.0026 | 0.300532 | 0.150266 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150266 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(194\) | − | 53.7285i | − | 0.276951i | ||||||
\(195\) | 11.5716i | 0.0593415i | ||||||||
\(196\) | −162.849 | −0.830860 | ||||||||
\(197\) | 96.0748 | 0.487689 | 0.243845 | − | 0.969814i | \(-0.421591\pi\) | ||||
0.243845 | + | 0.969814i | \(0.421591\pi\) | |||||||
\(198\) | 58.8552i | 0.297249i | ||||||||
\(199\) | − | 198.494i | − | 0.997459i | −0.866758 | − | 0.498729i | \(-0.833800\pi\) | ||
0.866758 | − | 0.498729i | \(-0.166200\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | − | 101.349i | − | 0.504224i | ||||||
\(202\) | −208.547 | −1.03241 | ||||||||
\(203\) | 132.740i | 0.653893i | ||||||||
\(204\) | 53.1436i | 0.260508i | ||||||||
\(205\) | − | 81.2198i | − | 0.396194i | ||||||
\(206\) | − | 105.784i | − | 0.513513i | ||||||
\(207\) | −62.7740 | − | 28.6430i | −0.303256 | − | 0.138372i | ||||
\(208\) | −11.9511 | −0.0574571 | ||||||||
\(209\) | 35.0889 | 0.167889 | ||||||||
\(210\) | 62.5518 | 0.297866 | ||||||||
\(211\) | −154.074 | −0.730207 | −0.365103 | − | 0.930967i | \(-0.618966\pi\) | ||||
−0.365103 | + | 0.930967i | \(0.618966\pi\) | |||||||
\(212\) | − | 118.990i | − | 0.561275i | ||||||
\(213\) | 174.224 | 0.817952 | ||||||||
\(214\) | − | 52.1697i | − | 0.243784i | ||||||
\(215\) | −44.6584 | −0.207713 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 30.9728i | 0.142732i | ||||||||
\(218\) | − | 126.131i | − | 0.578584i | ||||||
\(219\) | −29.0282 | −0.132549 | ||||||||
\(220\) | 62.0388 | 0.281995 | ||||||||
\(221\) | − | 45.8361i | − | 0.207403i | ||||||
\(222\) | 77.8220i | 0.350550i | ||||||||
\(223\) | −88.2708 | −0.395833 | −0.197916 | − | 0.980219i | \(-0.563417\pi\) | ||||
−0.197916 | + | 0.980219i | \(0.563417\pi\) | |||||||
\(224\) | 64.6032i | 0.288407i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 56.1638i | 0.248512i | ||||||||
\(227\) | 220.495i | 0.971345i | 0.874141 | + | 0.485673i | \(0.161425\pi\) | ||||
−0.874141 | + | 0.485673i | \(0.838575\pi\) | |||||||
\(228\) | − | 8.76216i | − | 0.0384305i | ||||||
\(229\) | 138.113i | 0.603115i | 0.953448 | + | 0.301557i | \(0.0975065\pi\) | ||||
−0.953448 | + | 0.301557i | \(0.902494\pi\) | |||||||
\(230\) | −30.1924 | + | 66.1696i | −0.131271 | + | 0.287694i | ||||
\(231\) | −274.403 | −1.18789 | ||||||||
\(232\) | 32.8752 | 0.141703 | ||||||||
\(233\) | 98.1877 | 0.421406 | 0.210703 | − | 0.977550i | \(-0.432425\pi\) | ||||
0.210703 | + | 0.977550i | \(0.432425\pi\) | |||||||
\(234\) | −12.6760 | −0.0541711 | ||||||||
\(235\) | − | 116.794i | − | 0.496995i | ||||||
\(236\) | 163.213 | 0.691581 | ||||||||
\(237\) | − | 105.048i | − | 0.443240i | ||||||
\(238\) | −247.773 | −1.04106 | ||||||||
\(239\) | −421.219 | −1.76242 | −0.881211 | − | 0.472722i | \(-0.843271\pi\) | ||||
−0.881211 | + | 0.472722i | \(0.843271\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | − | 181.752i | − | 0.754160i | −0.926181 | − | 0.377080i | \(-0.876928\pi\) | ||
0.926181 | − | 0.377080i | \(-0.123072\pi\) | |||||||
\(242\) | −101.033 | −0.417491 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 84.4272i | 0.346013i | ||||||||
\(245\) | 182.070i | 0.743144i | ||||||||
\(246\) | 88.9718 | 0.361674 | ||||||||
\(247\) | 7.55732i | 0.0305964i | ||||||||
\(248\) | 7.67089 | 0.0309310 | ||||||||
\(249\) | − | 76.4752i | − | 0.307130i | ||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | − | 208.037i | − | 0.828835i | −0.910087 | − | 0.414417i | \(-0.863985\pi\) | ||
0.910087 | − | 0.414417i | \(-0.136015\pi\) | |||||||
\(252\) | 68.5221i | 0.271913i | ||||||||
\(253\) | 132.448 | − | 290.273i | 0.523511 | − | 1.14733i | ||||
\(254\) | −184.775 | −0.727460 | ||||||||
\(255\) | 59.4164 | 0.233005 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −463.102 | −1.80196 | −0.900978 | − | 0.433866i | \(-0.857149\pi\) | ||||
−0.900978 | + | 0.433866i | \(0.857149\pi\) | |||||||
\(258\) | − | 48.9208i | − | 0.189615i | ||||||
\(259\) | −362.832 | −1.40090 | ||||||||
\(260\) | 13.3617i | 0.0513912i | ||||||||
\(261\) | 34.8694 | 0.133599 | ||||||||
\(262\) | 4.22548 | 0.0161278 | ||||||||
\(263\) | − | 34.0014i | − | 0.129283i | −0.997909 | − | 0.0646415i | \(-0.979410\pi\) | ||
0.997909 | − | 0.0646415i | \(-0.0205904\pi\) | |||||||
\(264\) | 67.9602i | 0.257425i | ||||||||
\(265\) | −133.035 | −0.502020 | ||||||||
\(266\) | 40.8521 | 0.153579 | ||||||||
\(267\) | 184.022i | 0.689219i | ||||||||
\(268\) | − | 117.028i | − | 0.436671i | ||||||
\(269\) | 499.913 | 1.85841 | 0.929207 | − | 0.369560i | \(-0.120491\pi\) | ||||
0.929207 | + | 0.369560i | \(0.120491\pi\) | |||||||
\(270\) | − | 16.4317i | − | 0.0608581i | ||||||
\(271\) | 246.666 | 0.910207 | 0.455104 | − | 0.890439i | \(-0.349602\pi\) | ||||
0.455104 | + | 0.890439i | \(0.349602\pi\) | |||||||
\(272\) | 61.3650i | 0.225607i | ||||||||
\(273\) | − | 59.1000i | − | 0.216483i | ||||||
\(274\) | 169.956i | 0.620279i | ||||||||
\(275\) | − | 69.3615i | − | 0.252224i | ||||||
\(276\) | −72.4852 | − | 33.0741i | −0.262627 | − | 0.119834i | ||||
\(277\) | −350.841 | −1.26657 | −0.633287 | − | 0.773917i | \(-0.718295\pi\) | ||||
−0.633287 | + | 0.773917i | \(0.718295\pi\) | |||||||
\(278\) | −179.990 | −0.647447 | ||||||||
\(279\) | 8.13621 | 0.0291620 | ||||||||
\(280\) | 72.2286 | 0.257959 | ||||||||
\(281\) | 232.377i | 0.826965i | 0.910512 | + | 0.413482i | \(0.135688\pi\) | ||||
−0.910512 | + | 0.413482i | \(0.864312\pi\) | |||||||
\(282\) | 127.941 | 0.453692 | ||||||||
\(283\) | − | 462.787i | − | 1.63529i | −0.575723 | − | 0.817645i | \(-0.695279\pi\) | ||
0.575723 | − | 0.817645i | \(-0.304721\pi\) | |||||||
\(284\) | 201.176 | 0.708367 | ||||||||
\(285\) | −9.79639 | −0.0343733 | ||||||||
\(286\) | − | 58.6153i | − | 0.204949i | ||||||
\(287\) | 414.817i | 1.44535i | ||||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 53.6463 | 0.185627 | ||||||||
\(290\) | − | 36.7556i | − | 0.126743i | ||||||
\(291\) | − | 65.8037i | − | 0.226130i | ||||||
\(292\) | −33.5189 | −0.114791 | ||||||||
\(293\) | 163.785i | 0.558995i | 0.960146 | + | 0.279497i | \(0.0901678\pi\) | ||||
−0.960146 | + | 0.279497i | \(0.909832\pi\) | |||||||
\(294\) | −199.448 | −0.678394 | ||||||||
\(295\) | − | 182.478i | − | 0.618568i | ||||||
\(296\) | 89.8611i | 0.303585i | ||||||||
\(297\) | 72.0826i | 0.242702i | ||||||||
\(298\) | 186.168i | 0.624725i | ||||||||
\(299\) | 62.5181 | + | 28.5263i | 0.209091 | + | 0.0954056i | ||||
\(300\) | −17.3205 | −0.0577350 | ||||||||
\(301\) | 228.085 | 0.757758 | ||||||||
\(302\) | 210.909 | 0.698374 | ||||||||
\(303\) | −255.416 | −0.842959 | ||||||||
\(304\) | − | 10.1177i | − | 0.0332818i | ||||||
\(305\) | 94.3924 | 0.309483 | ||||||||
\(306\) | 65.0874i | 0.212704i | ||||||||
\(307\) | −359.655 | −1.17152 | −0.585758 | − | 0.810486i | \(-0.699203\pi\) | ||||
−0.585758 | + | 0.810486i | \(0.699203\pi\) | |||||||
\(308\) | −316.853 | −1.02874 | ||||||||
\(309\) | − | 129.558i | − | 0.419281i | ||||||
\(310\) | − | 8.57632i | − | 0.0276655i | ||||||
\(311\) | 314.588 | 1.01154 | 0.505768 | − | 0.862669i | \(-0.331209\pi\) | ||||
0.505768 | + | 0.862669i | \(0.331209\pi\) | |||||||
\(312\) | −14.6370 | −0.0469136 | ||||||||
\(313\) | − | 451.729i | − | 1.44322i | −0.692298 | − | 0.721612i | \(-0.743401\pi\) | ||
0.692298 | − | 0.721612i | \(-0.256599\pi\) | |||||||
\(314\) | − | 322.706i | − | 1.02773i | ||||||
\(315\) | 76.6100 | 0.243206 | ||||||||
\(316\) | − | 121.299i | − | 0.383858i | ||||||
\(317\) | 179.052 | 0.564834 | 0.282417 | − | 0.959292i | \(-0.408864\pi\) | ||||
0.282417 | + | 0.959292i | \(0.408864\pi\) | |||||||
\(318\) | − | 145.733i | − | 0.458279i | ||||||
\(319\) | 161.240i | 0.505454i | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 63.8946i | − | 0.199048i | ||||||
\(322\) | 154.203 | − | 337.950i | 0.478891 | − | 1.04954i | ||||
\(323\) | 38.8044 | 0.120138 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 14.9389 | 0.0459657 | ||||||||
\(326\) | 368.454 | 1.13023 | ||||||||
\(327\) | − | 154.479i | − | 0.472412i | ||||||
\(328\) | 102.736 | 0.313219 | ||||||||
\(329\) | 596.505i | 1.81309i | ||||||||
\(330\) | 75.9818 | 0.230248 | ||||||||
\(331\) | 528.798 | 1.59758 | 0.798788 | − | 0.601612i | \(-0.205475\pi\) | ||||
0.798788 | + | 0.601612i | \(0.205475\pi\) | |||||||
\(332\) | − | 88.3060i | − | 0.265982i | ||||||
\(333\) | 95.3121i | 0.286223i | ||||||||
\(334\) | −250.472 | −0.749916 | ||||||||
\(335\) | −130.841 | −0.390570 | ||||||||
\(336\) | 79.1225i | 0.235484i | ||||||||
\(337\) | 493.496i | 1.46438i | 0.681100 | + | 0.732191i | \(0.261502\pi\) | ||||
−0.681100 | + | 0.732191i | \(0.738498\pi\) | |||||||
\(338\) | −226.378 | −0.669757 | ||||||||
\(339\) | 68.7863i | 0.202910i | ||||||||
\(340\) | 68.6081 | 0.201789 | ||||||||
\(341\) | 37.6227i | 0.110330i | ||||||||
\(342\) | − | 10.7314i | − | 0.0313784i | ||||||
\(343\) | − | 370.297i | − | 1.07958i | ||||||
\(344\) | − | 56.4889i | − | 0.164212i | ||||||
\(345\) | −36.9780 | + | 81.0409i | −0.107183 | + | 0.234901i | ||||
\(346\) | 10.7607 | 0.0311003 | ||||||||
\(347\) | 133.171 | 0.383778 | 0.191889 | − | 0.981417i | \(-0.438539\pi\) | ||||
0.191889 | + | 0.981417i | \(0.438539\pi\) | |||||||
\(348\) | 40.2637 | 0.115700 | ||||||||
\(349\) | 62.9714 | 0.180434 | 0.0902169 | − | 0.995922i | \(-0.471244\pi\) | ||||
0.0902169 | + | 0.995922i | \(0.471244\pi\) | |||||||
\(350\) | − | 80.7540i | − | 0.230726i | ||||||
\(351\) | −15.5249 | −0.0442305 | ||||||||
\(352\) | 78.4736i | 0.222936i | ||||||||
\(353\) | −103.337 | −0.292739 | −0.146370 | − | 0.989230i | \(-0.546759\pi\) | ||||
−0.146370 | + | 0.989230i | \(0.546759\pi\) | |||||||
\(354\) | 199.894 | 0.564673 | ||||||||
\(355\) | − | 224.922i | − | 0.633583i | ||||||
\(356\) | 212.490i | 0.596881i | ||||||||
\(357\) | −303.459 | −0.850026 | ||||||||
\(358\) | 451.677 | 1.26167 | ||||||||
\(359\) | − | 608.721i | − | 1.69560i | −0.530314 | − | 0.847801i | \(-0.677926\pi\) | ||
0.530314 | − | 0.847801i | \(-0.322074\pi\) | |||||||
\(360\) | − | 18.9737i | − | 0.0527046i | ||||||
\(361\) | 354.602 | 0.982277 | ||||||||
\(362\) | − | 162.862i | − | 0.449895i | ||||||
\(363\) | −123.739 | −0.340880 | ||||||||
\(364\) | − | 68.2428i | − | 0.187480i | ||||||
\(365\) | 37.4753i | 0.102672i | ||||||||
\(366\) | 103.402i | 0.282518i | ||||||||
\(367\) | 213.718i | 0.582338i | 0.956672 | + | 0.291169i | \(0.0940441\pi\) | ||||
−0.956672 | + | 0.291169i | \(0.905956\pi\) | |||||||
\(368\) | −83.6987 | − | 38.1907i | −0.227442 | − | 0.103779i | ||||
\(369\) | 108.968 | 0.295306 | ||||||||
\(370\) | 100.468 | 0.271535 | ||||||||
\(371\) | 679.455 | 1.83142 | ||||||||
\(372\) | 9.39489 | 0.0252551 | ||||||||
\(373\) | − | 542.556i | − | 1.45457i | −0.686334 | − | 0.727287i | \(-0.740781\pi\) | ||
0.686334 | − | 0.727287i | \(-0.259219\pi\) | |||||||
\(374\) | −300.971 | −0.804735 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | 147.734 | 0.392909 | ||||||||
\(377\) | −34.7273 | −0.0921148 | ||||||||
\(378\) | 83.9221i | 0.222016i | ||||||||
\(379\) | 348.769i | 0.920235i | 0.887858 | + | 0.460117i | \(0.152193\pi\) | ||||
−0.887858 | + | 0.460117i | \(0.847807\pi\) | |||||||
\(380\) | −11.3119 | −0.0297682 | ||||||||
\(381\) | −226.302 | −0.593969 | ||||||||
\(382\) | − | 148.041i | − | 0.387543i | ||||||
\(383\) | 672.210i | 1.75512i | 0.479470 | + | 0.877559i | \(0.340829\pi\) | ||||
−0.479470 | + | 0.877559i | \(0.659171\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 354.253i | 0.920136i | ||||||||
\(386\) | 82.0281 | 0.212508 | ||||||||
\(387\) | − | 59.9155i | − | 0.154820i | ||||||
\(388\) | − | 75.9836i | − | 0.195834i | ||||||
\(389\) | 464.622i | 1.19440i | 0.802092 | + | 0.597200i | \(0.203720\pi\) | ||||
−0.802092 | + | 0.597200i | \(0.796280\pi\) | |||||||
\(390\) | 16.3647i | 0.0419608i | ||||||||
\(391\) | 146.473 | − | 321.010i | 0.374612 | − | 0.820999i | ||||
\(392\) | −230.303 | −0.587507 | ||||||||
\(393\) | 5.17513 | 0.0131683 | ||||||||
\(394\) | 135.870 | 0.344848 | ||||||||
\(395\) | −135.616 | −0.343333 | ||||||||
\(396\) | 83.2338i | 0.210186i | ||||||||
\(397\) | −1.92370 | −0.00484560 | −0.00242280 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242280 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(398\) | − | 280.713i | − | 0.705310i | ||||||
\(399\) | 50.0335 | 0.125397 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 417.281i | 1.04060i | 0.853983 | + | 0.520301i | \(0.174180\pi\) | ||||
−0.853983 | + | 0.520301i | \(0.825820\pi\) | |||||||
\(402\) | − | 143.329i | − | 0.356540i | ||||||
\(403\) | −8.10305 | −0.0201068 | ||||||||
\(404\) | −294.930 | −0.730024 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | 187.723i | 0.462372i | ||||||||
\(407\) | −440.733 | −1.08288 | ||||||||
\(408\) | 75.1564i | 0.184207i | ||||||||
\(409\) | −812.820 | −1.98733 | −0.993667 | − | 0.112361i | \(-0.964159\pi\) | ||||
−0.993667 | + | 0.112361i | \(0.964159\pi\) | |||||||
\(410\) | − | 114.862i | − | 0.280152i | ||||||
\(411\) | 208.153i | 0.506455i | ||||||||
\(412\) | − | 149.601i | − | 0.363108i | ||||||
\(413\) | 931.974i | 2.25660i | ||||||||
\(414\) | −88.7759 | − | 40.5074i | −0.214434 | − | 0.0978439i | ||||
\(415\) | −98.7291 | −0.237901 | ||||||||
\(416\) | −16.9014 | −0.0406283 | ||||||||
\(417\) | −220.442 | −0.528638 | ||||||||
\(418\) | 49.6232 | 0.118716 | ||||||||
\(419\) | − | 268.155i | − | 0.639988i | −0.947420 | − | 0.319994i | \(-0.896319\pi\) | ||
0.947420 | − | 0.319994i | \(-0.103681\pi\) | |||||||
\(420\) | 88.4616 | 0.210623 | ||||||||
\(421\) | 174.098i | 0.413533i | 0.978390 | + | 0.206767i | \(0.0662941\pi\) | ||||
−0.978390 | + | 0.206767i | \(0.933706\pi\) | |||||||
\(422\) | −217.893 | −0.516334 | ||||||||
\(423\) | 156.695 | 0.370438 | ||||||||
\(424\) | − | 168.278i | − | 0.396881i | ||||||
\(425\) | − | 76.7062i | − | 0.180485i | ||||||
\(426\) | 246.390 | 0.578380 | ||||||||
\(427\) | −482.094 | −1.12903 | ||||||||
\(428\) | − | 73.7791i | − | 0.172381i | ||||||
\(429\) | − | 71.7888i | − | 0.167340i | ||||||
\(430\) | −63.1565 | −0.146876 | ||||||||
\(431\) | − | 291.962i | − | 0.677407i | −0.940893 | − | 0.338704i | \(-0.890012\pi\) | ||
0.940893 | − | 0.338704i | \(-0.109988\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 439.111i | 1.01411i | 0.861913 | + | 0.507056i | \(0.169266\pi\) | ||||
−0.861913 | + | 0.507056i | \(0.830734\pi\) | |||||||
\(434\) | 43.8021i | 0.100927i | ||||||||
\(435\) | − | 45.0162i | − | 0.103486i | ||||||
\(436\) | − | 178.377i | − | 0.409121i | ||||||
\(437\) | −24.1501 | + | 52.9272i | −0.0552633 | + | 0.121115i | ||||
\(438\) | −41.0521 | −0.0937263 | ||||||||
\(439\) | −62.0644 | −0.141377 | −0.0706884 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706884 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(440\) | 87.7362 | 0.199400 | ||||||||
\(441\) | −244.273 | −0.553907 | ||||||||
\(442\) | − | 64.8221i | − | 0.146656i | ||||||
\(443\) | −261.415 | −0.590102 | −0.295051 | − | 0.955482i | \(-0.595337\pi\) | ||||
−0.295051 | + | 0.955482i | \(0.595337\pi\) | |||||||
\(444\) | 110.057i | 0.247876i | ||||||||
\(445\) | 237.571 | 0.533867 | ||||||||
\(446\) | −124.834 | −0.279896 | ||||||||
\(447\) | 228.008i | 0.510086i | ||||||||
\(448\) | 91.3628i | 0.203935i | ||||||||
\(449\) | 431.325 | 0.960634 | 0.480317 | − | 0.877095i | \(-0.340522\pi\) | ||||
0.480317 | + | 0.877095i | \(0.340522\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | 503.878i | 1.11725i | ||||||||
\(452\) | 79.4276i | 0.175725i | ||||||||
\(453\) | 258.310 | 0.570220 | ||||||||
\(454\) | 311.828i | 0.686845i | ||||||||
\(455\) | −76.2977 | −0.167687 | ||||||||
\(456\) | − | 12.3916i | − | 0.0271745i | ||||||
\(457\) | 734.574i | 1.60738i | 0.595046 | + | 0.803692i | \(0.297134\pi\) | ||||
−0.595046 | + | 0.803692i | \(0.702866\pi\) | |||||||
\(458\) | 195.322i | 0.426466i | ||||||||
\(459\) | 79.7154i | 0.173672i | ||||||||
\(460\) | −42.6985 | + | 93.5780i | −0.0928229 | + | 0.203430i | ||||
\(461\) | 626.021 | 1.35796 | 0.678982 | − | 0.734155i | \(-0.262422\pi\) | ||||
0.678982 | + | 0.734155i | \(0.262422\pi\) | |||||||
\(462\) | −388.064 | −0.839966 | ||||||||
\(463\) | −320.725 | −0.692712 | −0.346356 | − | 0.938103i | \(-0.612581\pi\) | ||||
−0.346356 | + | 0.938103i | \(0.612581\pi\) | |||||||
\(464\) | 46.4925 | 0.100199 | ||||||||
\(465\) | − | 10.5038i | − | 0.0225888i | ||||||
\(466\) | 138.858 | 0.297979 | ||||||||
\(467\) | 148.416i | 0.317807i | 0.987294 | + | 0.158904i | \(0.0507959\pi\) | ||||
−0.987294 | + | 0.158904i | \(0.949204\pi\) | |||||||
\(468\) | −17.9266 | −0.0383048 | ||||||||
\(469\) | 668.249 | 1.42484 | ||||||||
\(470\) | − | 165.171i | − | 0.351429i | ||||||
\(471\) | − | 395.233i | − | 0.839136i | ||||||
\(472\) | 230.818 | 0.489021 | ||||||||
\(473\) | 277.055 | 0.585741 | ||||||||
\(474\) | − | 148.560i | − | 0.313418i | ||||||
\(475\) | 12.6471i | 0.0266255i | ||||||||
\(476\) | −350.405 | −0.736144 | ||||||||
\(477\) | − | 178.486i | − | 0.374183i | ||||||
\(478\) | −595.694 | −1.24622 | ||||||||
\(479\) | − | 749.170i | − | 1.56403i | −0.623260 | − | 0.782014i | \(-0.714192\pi\) | ||
0.623260 | − | 0.782014i | \(-0.285808\pi\) | |||||||
\(480\) | − | 21.9089i | − | 0.0456435i | ||||||
\(481\) | − | 94.9236i | − | 0.197346i | ||||||
\(482\) | − | 257.037i | − | 0.533271i | ||||||
\(483\) | 188.859 | − | 413.903i | 0.391012 | − | 0.856942i | ||||
\(484\) | −142.882 | −0.295210 | ||||||||
\(485\) | −84.9523 | −0.175159 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 289.122 | 0.593679 | 0.296839 | − | 0.954927i | \(-0.404067\pi\) | ||||
0.296839 | + | 0.954927i | \(0.404067\pi\) | |||||||
\(488\) | 119.398i | 0.244668i | ||||||||
\(489\) | 451.262 | 0.922827 | ||||||||
\(490\) | 257.486i | 0.525482i | ||||||||
\(491\) | 768.805 | 1.56579 | 0.782897 | − | 0.622152i | \(-0.213741\pi\) | ||||
0.782897 | + | 0.622152i | \(0.213741\pi\) | |||||||
\(492\) | 125.825 | 0.255742 | ||||||||
\(493\) | 178.313i | 0.361690i | ||||||||
\(494\) | 10.6877i | 0.0216350i | ||||||||
\(495\) | 93.0583 | 0.187997 | ||||||||
\(496\) | 10.8483 | 0.0218715 | ||||||||
\(497\) | 1148.75i | 2.31137i | ||||||||
\(498\) | − | 108.152i | − | 0.217173i | ||||||
\(499\) | 201.586 | 0.403981 | 0.201990 | − | 0.979388i | \(-0.435259\pi\) | ||||
0.201990 | + | 0.979388i | \(0.435259\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −306.764 | −0.612304 | ||||||||
\(502\) | − | 294.209i | − | 0.586075i | ||||||
\(503\) | 385.180i | 0.765766i | 0.923797 | + | 0.382883i | \(0.125069\pi\) | ||||
−0.923797 | + | 0.382883i | \(0.874931\pi\) | |||||||
\(504\) | 96.9048i | 0.192272i | ||||||||
\(505\) | 329.741i | 0.652953i | ||||||||
\(506\) | 187.310 | − | 410.509i | 0.370178 | − | 0.811282i | ||||
\(507\) | −277.255 | −0.546854 | ||||||||
\(508\) | −261.311 | −0.514392 | ||||||||
\(509\) | 563.072 | 1.10623 | 0.553116 | − | 0.833104i | \(-0.313439\pi\) | ||||
0.553116 | + | 0.833104i | \(0.313439\pi\) | |||||||
\(510\) | 84.0274 | 0.164760 | ||||||||
\(511\) | − | 191.399i | − | 0.374557i | ||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 13.1432i | − | 0.0256204i | ||||||
\(514\) | −654.926 | −1.27417 | ||||||||
\(515\) | −167.259 | −0.324774 | ||||||||
\(516\) | − | 69.1844i | − | 0.134078i | ||||||
\(517\) | 724.576i | 1.40150i | ||||||||
\(518\) | −513.122 | −0.990584 | ||||||||
\(519\) | 13.1791 | 0.0253933 | ||||||||
\(520\) | 18.8963i | 0.0363391i | ||||||||
\(521\) | − | 687.431i | − | 1.31945i | −0.751509 | − | 0.659723i | \(-0.770674\pi\) | ||
0.751509 | − | 0.659723i | \(-0.229326\pi\) | |||||||
\(522\) | 49.3128 | 0.0944689 | ||||||||
\(523\) | 580.256i | 1.10948i | 0.832025 | + | 0.554738i | \(0.187181\pi\) | ||||
−0.832025 | + | 0.554738i | \(0.812819\pi\) | |||||||
\(524\) | 5.97573 | 0.0114041 | ||||||||
\(525\) | − | 98.9031i | − | 0.188387i | ||||||
\(526\) | − | 48.0853i | − | 0.0914169i | ||||||
\(527\) | 41.6065i | 0.0789498i | ||||||||
\(528\) | 96.1102i | 0.182027i | ||||||||
\(529\) | 346.684 | + | 399.564i | 0.655357 | + | 0.755320i | ||||
\(530\) | −188.140 | −0.354982 | ||||||||
\(531\) | 244.819 | 0.461054 | ||||||||
\(532\) | 57.7737 | 0.108597 | ||||||||
\(533\) | −108.524 | −0.203609 | ||||||||
\(534\) | 260.246i | 0.487352i | ||||||||
\(535\) | −82.4875 | −0.154182 | ||||||||
\(536\) | − | 165.502i | − | 0.308773i | ||||||
\(537\) | 553.189 | 1.03015 | ||||||||
\(538\) | 706.984 | 1.31410 | ||||||||
\(539\) | − | 1129.54i | − | 2.09563i | ||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | 148.687 | 0.274838 | 0.137419 | − | 0.990513i | \(-0.456119\pi\) | ||||
0.137419 | + | 0.990513i | \(0.456119\pi\) | |||||||
\(542\) | 348.839 | 0.643614 | ||||||||
\(543\) | − | 199.465i | − | 0.367338i | ||||||
\(544\) | 86.7832i | 0.159528i | ||||||||
\(545\) | −199.431 | −0.365929 | ||||||||
\(546\) | − | 83.5800i | − | 0.153077i | ||||||
\(547\) | −648.445 | −1.18546 | −0.592729 | − | 0.805402i | \(-0.701949\pi\) | ||||
−0.592729 | + | 0.805402i | \(0.701949\pi\) | |||||||
\(548\) | 240.355i | 0.438603i | ||||||||
\(549\) | 126.641i | 0.230675i | ||||||||
\(550\) | − | 98.0920i | − | 0.178349i | ||||||
\(551\) | − | 29.3998i | − | 0.0533571i | ||||||
\(552\) | −102.510 | − | 46.7739i | −0.185706 | − | 0.0847353i | ||||
\(553\) | 692.638 | 1.25251 | ||||||||
\(554\) | −496.164 | −0.895603 | ||||||||
\(555\) | 123.047 | 0.221707 | ||||||||
\(556\) | −254.545 | −0.457814 | ||||||||
\(557\) | − | 697.203i | − | 1.25171i | −0.779939 | − | 0.625856i | \(-0.784750\pi\) | ||
0.779939 | − | 0.625856i | \(-0.215250\pi\) | |||||||
\(558\) | 11.5063 | 0.0206207 | ||||||||
\(559\) | 59.6713i | 0.106746i | ||||||||
\(560\) | 102.147 | 0.182405 | ||||||||
\(561\) | −368.612 | −0.657063 | ||||||||
\(562\) | 328.631i | 0.584752i | ||||||||
\(563\) | 890.248i | 1.58126i | 0.612295 | + | 0.790629i | \(0.290246\pi\) | ||||
−0.612295 | + | 0.790629i | \(0.709754\pi\) | |||||||
\(564\) | 180.936 | 0.320809 | ||||||||
\(565\) | 88.8028 | 0.157173 | ||||||||
\(566\) | − | 654.480i | − | 1.15632i | ||||||
\(567\) | 102.783i | 0.181275i | ||||||||
\(568\) | 284.506 | 0.500891 | ||||||||
\(569\) | 548.456i | 0.963894i | 0.876200 | + | 0.481947i | \(0.160070\pi\) | ||||
−0.876200 | + | 0.481947i | \(0.839930\pi\) | |||||||
\(570\) | −13.8542 | −0.0243056 | ||||||||
\(571\) | − | 479.794i | − | 0.840270i | −0.907462 | − | 0.420135i | \(-0.861983\pi\) | ||
0.907462 | − | 0.420135i | \(-0.138017\pi\) | |||||||
\(572\) | − | 82.8946i | − | 0.144921i | ||||||
\(573\) | − | 181.313i | − | 0.316427i | ||||||
\(574\) | 586.639i | 1.02202i | ||||||||
\(575\) | 104.623 | + | 47.7384i | 0.181954 | + | 0.0830233i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 12.3741 | 0.0214456 | 0.0107228 | − | 0.999943i | \(-0.496587\pi\) | ||||
0.0107228 | + | 0.999943i | \(0.496587\pi\) | |||||||
\(578\) | 75.8673 | 0.131258 | ||||||||
\(579\) | 100.464 | 0.173512 | ||||||||
\(580\) | − | 51.9802i | − | 0.0896211i | ||||||
\(581\) | 504.243 | 0.867887 | ||||||||
\(582\) | − | 93.0605i | − | 0.159898i | ||||||
\(583\) | 825.335 | 1.41567 | ||||||||
\(584\) | −47.4029 | −0.0811694 | ||||||||
\(585\) | 20.0426i | 0.0342608i | ||||||||
\(586\) | 231.628i | 0.395269i | ||||||||
\(587\) | 613.203 | 1.04464 | 0.522320 | − | 0.852750i | \(-0.325067\pi\) | ||||
0.522320 | + | 0.852750i | \(0.325067\pi\) | |||||||
\(588\) | −282.062 | −0.479697 | ||||||||
\(589\) | − | 6.85996i | − | 0.0116468i | ||||||
\(590\) | − | 258.062i | − | 0.437394i | ||||||
\(591\) | 166.406 | 0.281568 | ||||||||
\(592\) | 127.083i | 0.214667i | ||||||||
\(593\) | −208.251 | −0.351182 | −0.175591 | − | 0.984463i | \(-0.556184\pi\) | ||||
−0.175591 | + | 0.984463i | \(0.556184\pi\) | |||||||
\(594\) | 101.940i | 0.171617i | ||||||||
\(595\) | 391.764i | 0.658427i | ||||||||
\(596\) | 263.281i | 0.441747i | ||||||||
\(597\) | − | 343.802i | − | 0.575883i | ||||||
\(598\) | 88.4140 | + | 40.3423i | 0.147849 | + | 0.0674620i | ||||
\(599\) | 925.513 | 1.54510 | 0.772548 | − | 0.634956i | \(-0.218982\pi\) | ||||
0.772548 | + | 0.634956i | \(0.218982\pi\) | |||||||
\(600\) | −24.4949 | −0.0408248 | ||||||||
\(601\) | −922.104 | −1.53428 | −0.767142 | − | 0.641478i | \(-0.778322\pi\) | ||||
−0.767142 | + | 0.641478i | \(0.778322\pi\) | |||||||
\(602\) | 322.561 | 0.535816 | ||||||||
\(603\) | − | 175.542i | − | 0.291114i | ||||||
\(604\) | 298.270 | 0.493825 | ||||||||
\(605\) | 159.747i | 0.264044i | ||||||||
\(606\) | −361.213 | −0.596062 | ||||||||
\(607\) | −73.7934 | −0.121571 | −0.0607853 | − | 0.998151i | \(-0.519360\pi\) | ||||
−0.0607853 | + | 0.998151i | \(0.519360\pi\) | |||||||
\(608\) | − | 14.3085i | − | 0.0235338i | ||||||
\(609\) | 229.913i | 0.377525i | ||||||||
\(610\) | 133.491 | 0.218838 | ||||||||
\(611\) | −156.057 | −0.255412 | ||||||||
\(612\) | 92.0475i | 0.150404i | ||||||||
\(613\) | 808.004i | 1.31811i | 0.752093 | + | 0.659057i | \(0.229044\pi\) | ||||
−0.752093 | + | 0.659057i | \(0.770956\pi\) | |||||||
\(614\) | −508.629 | −0.828387 | ||||||||
\(615\) | − | 140.677i | − | 0.228743i | ||||||
\(616\) | −448.098 | −0.727432 | ||||||||
\(617\) | − | 484.018i | − | 0.784470i | −0.919865 | − | 0.392235i | \(-0.871702\pi\) | ||
0.919865 | − | 0.392235i | \(-0.128298\pi\) | |||||||
\(618\) | − | 183.223i | − | 0.296477i | ||||||
\(619\) | 454.285i | 0.733902i | 0.930240 | + | 0.366951i | \(0.119598\pi\) | ||||
−0.930240 | + | 0.366951i | \(0.880402\pi\) | |||||||
\(620\) | − | 12.1287i | − | 0.0195625i | ||||||
\(621\) | −108.728 | − | 49.6112i | −0.175085 | − | 0.0798892i | ||||
\(622\) | 444.895 | 0.715265 | ||||||||
\(623\) | −1213.35 | −1.94760 | ||||||||
\(624\) | −20.6999 | −0.0331729 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 638.841i | − | 1.02051i | ||||||
\(627\) | 60.7757 | 0.0969309 | ||||||||
\(628\) | − | 456.376i | − | 0.726713i | ||||||
\(629\) | −487.402 | −0.774884 | ||||||||
\(630\) | 108.343 | 0.171973 | ||||||||
\(631\) | 385.780i | 0.611380i | 0.952131 | + | 0.305690i | \(0.0988870\pi\) | ||||
−0.952131 | + | 0.305690i | \(0.901113\pi\) | |||||||
\(632\) | − | 171.543i | − | 0.271428i | ||||||
\(633\) | −266.863 | −0.421585 | ||||||||
\(634\) | 253.218 | 0.399398 | ||||||||
\(635\) | 292.155i | 0.460086i | ||||||||
\(636\) | − | 206.097i | − | 0.324052i | ||||||
\(637\) | 243.277 | 0.381911 | ||||||||
\(638\) | 228.027i | 0.357410i | ||||||||
\(639\) | 301.765 | 0.472245 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | 1009.69i | 1.57518i | 0.616199 | + | 0.787591i | \(0.288672\pi\) | ||||
−0.616199 | + | 0.787591i | \(0.711328\pi\) | |||||||
\(642\) | − | 90.3606i | − | 0.140749i | ||||||
\(643\) | 849.482i | 1.32112i | 0.750772 | + | 0.660561i | \(0.229682\pi\) | ||||
−0.750772 | + | 0.660561i | \(0.770318\pi\) | |||||||
\(644\) | 218.076 | − | 477.934i | 0.338627 | − | 0.742133i | ||||
\(645\) | −77.3506 | −0.119923 | ||||||||
\(646\) | 54.8777 | 0.0849501 | ||||||||
\(647\) | −788.852 | −1.21924 | −0.609622 | − | 0.792692i | \(-0.708679\pi\) | ||||
−0.609622 | + | 0.792692i | \(0.708679\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 1132.07i | 1.74433i | ||||||||
\(650\) | 21.1267 | 0.0325027 | ||||||||
\(651\) | 53.6464i | 0.0824062i | ||||||||
\(652\) | 521.073 | 0.799191 | ||||||||
\(653\) | −912.671 | −1.39766 | −0.698830 | − | 0.715288i | \(-0.746295\pi\) | ||||
−0.698830 | + | 0.715288i | \(0.746295\pi\) | |||||||
\(654\) | − | 218.466i | − | 0.334046i | ||||||
\(655\) | − | 6.68107i | − | 0.0102001i | ||||||
\(656\) | 145.290 | 0.221479 | ||||||||
\(657\) | −50.2784 | −0.0765272 | ||||||||
\(658\) | 843.586i | 1.28205i | ||||||||
\(659\) | − | 845.536i | − | 1.28306i | −0.767098 | − | 0.641530i | \(-0.778300\pi\) | ||
0.767098 | − | 0.641530i | \(-0.221700\pi\) | |||||||
\(660\) | 107.454 | 0.162810 | ||||||||
\(661\) | − | 594.404i | − | 0.899250i | −0.893217 | − | 0.449625i | \(-0.851558\pi\) | ||
0.893217 | − | 0.449625i | \(-0.148442\pi\) | |||||||
\(662\) | 747.833 | 1.12966 | ||||||||
\(663\) | − | 79.3905i | − | 0.119744i | ||||||
\(664\) | − | 124.884i | − | 0.188078i | ||||||
\(665\) | − | 64.5929i | − | 0.0971322i | ||||||
\(666\) | 134.792i | 0.202390i | ||||||||
\(667\) | −243.210 | − | 110.974i | −0.364633 | − | 0.166378i | ||||
\(668\) | −354.221 | −0.530271 | ||||||||
\(669\) | −152.889 | −0.228534 | ||||||||
\(670\) | −185.037 | −0.276175 | ||||||||
\(671\) | −585.600 | −0.872727 | ||||||||
\(672\) | 111.896i | 0.166512i | ||||||||
\(673\) | −49.6946 | −0.0738404 | −0.0369202 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369202 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(674\) | 697.909i | 1.03547i | ||||||||
\(675\) | −25.9808 | −0.0384900 | ||||||||
\(676\) | −320.146 | −0.473589 | ||||||||
\(677\) | − | 256.435i | − | 0.378782i | −0.981902 | − | 0.189391i | \(-0.939349\pi\) | ||
0.981902 | − | 0.189391i | \(-0.0606513\pi\) | |||||||
\(678\) | 97.2786i | 0.143479i | ||||||||
\(679\) | 433.880 | 0.638998 | ||||||||
\(680\) | 97.0265 | 0.142686 | ||||||||
\(681\) | 381.909i | 0.560806i | ||||||||
\(682\) | 53.2065i | 0.0780154i | ||||||||
\(683\) | −1344.91 | −1.96912 | −0.984560 | − | 0.175045i | \(-0.943993\pi\) | ||||
−0.984560 | + | 0.175045i | \(0.943993\pi\) | |||||||
\(684\) | − | 15.1765i | − | 0.0221879i | ||||||
\(685\) | 268.725 | 0.392299 | ||||||||
\(686\) | − | 523.679i | − | 0.763380i | ||||||
\(687\) | 239.219i | 0.348208i | ||||||||
\(688\) | − | 79.8873i | − | 0.116115i | ||||||
\(689\) | 177.758i | 0.257994i | ||||||||
\(690\) | −52.2948 | + | 114.609i | −0.0757896 | + | 0.166100i | ||||
\(691\) | 559.144 | 0.809180 | 0.404590 | − | 0.914498i | \(-0.367414\pi\) | ||||
0.404590 | + | 0.914498i | \(0.367414\pi\) | |||||||
\(692\) | 15.2180 | 0.0219913 | ||||||||
\(693\) | −475.280 | −0.685829 | ||||||||
\(694\) | 188.332 | 0.271372 | ||||||||
\(695\) | 284.589i | 0.409481i | ||||||||
\(696\) | 56.9415 | 0.0818125 | ||||||||
\(697\) | 557.234i | 0.799475i | ||||||||
\(698\) | 89.0550 | 0.127586 | ||||||||
\(699\) | 170.066 | 0.243299 | ||||||||
\(700\) | − | 114.203i | − | 0.163148i | ||||||
\(701\) | 1187.16i | 1.69352i | 0.531977 | + | 0.846758i | \(0.321449\pi\) | ||||
−0.531977 | + | 0.846758i | \(0.678551\pi\) | |||||||
\(702\) | −21.9555 | −0.0312757 | ||||||||
\(703\) | 80.3614 | 0.114312 | ||||||||
\(704\) | 110.978i | 0.157640i | ||||||||
\(705\) | − | 202.293i | − | 0.286940i | ||||||
\(706\) | −146.140 | −0.206998 | ||||||||
\(707\) | − | 1684.10i | − | 2.38203i | ||||||
\(708\) | 282.693 | 0.399284 | ||||||||
\(709\) | − | 1093.87i | − | 1.54284i | −0.636325 | − | 0.771421i | \(-0.719546\pi\) | ||
0.636325 | − | 0.771421i | \(-0.280454\pi\) | |||||||
\(710\) | − | 318.088i | − | 0.448011i | ||||||
\(711\) | − | 181.948i | − | 0.255905i | ||||||
\(712\) | 300.506i | 0.422059i | ||||||||
\(713\) | −56.7492 | − | 25.8940i | −0.0795921 | − | 0.0363169i | ||||
\(714\) | −429.156 | −0.601059 | ||||||||
\(715\) | −92.6789 | −0.129621 | ||||||||
\(716\) | 638.767 | 0.892133 | ||||||||
\(717\) | −729.573 | −1.01754 | ||||||||
\(718\) | − | 860.862i | − | 1.19897i | ||||||
\(719\) | −1191.45 | −1.65709 | −0.828545 | − | 0.559923i | \(-0.810831\pi\) | ||||
−0.828545 | + | 0.559923i | \(0.810831\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | 854.245 | 1.18481 | ||||||||
\(722\) | 501.483 | 0.694575 | ||||||||
\(723\) | − | 314.804i | − | 0.435414i | ||||||
\(724\) | − | 230.322i | − | 0.318124i | ||||||
\(725\) | −58.1157 | −0.0801596 | ||||||||
\(726\) | −174.994 | −0.241038 | ||||||||
\(727\) | − | 1123.33i | − | 1.54516i | −0.634920 | − | 0.772578i | \(-0.718967\pi\) | ||
0.634920 | − | 0.772578i | \(-0.281033\pi\) | |||||||
\(728\) | − | 96.5098i | − | 0.132568i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 52.9981i | 0.0726001i | ||||||||
\(731\) | 306.393 | 0.419142 | ||||||||
\(732\) | 146.232i | 0.199771i | ||||||||
\(733\) | − | 81.6381i | − | 0.111375i | −0.998448 | − | 0.0556877i | \(-0.982265\pi\) | ||
0.998448 | − | 0.0556877i | \(-0.0177351\pi\) | |||||||
\(734\) | 302.243i | 0.411775i | ||||||||
\(735\) | 315.355i | 0.429054i | ||||||||
\(736\) | −118.368 | − | 54.0098i | −0.160826 | − | 0.0733829i | ||||
\(737\) | 811.723 | 1.10139 | ||||||||
\(738\) | 154.104 | 0.208813 | ||||||||
\(739\) | −706.438 | −0.955938 | −0.477969 | − | 0.878377i | \(-0.658627\pi\) | ||||
−0.477969 | + | 0.878377i | \(0.658627\pi\) | |||||||
\(740\) | 142.083 | 0.192004 | ||||||||
\(741\) | 13.0897i | 0.0176649i | ||||||||
\(742\) | 960.895 | 1.29501 | ||||||||
\(743\) | − | 1028.94i | − | 1.38484i | −0.721494 | − | 0.692420i | \(-0.756544\pi\) | ||
0.721494 | − | 0.692420i | \(-0.243456\pi\) | |||||||
\(744\) | 13.2864 | 0.0178580 | ||||||||
\(745\) | 294.357 | 0.395111 | ||||||||
\(746\) | − | 767.290i | − | 1.02854i | ||||||
\(747\) | − | 132.459i | − | 0.177321i | ||||||
\(748\) | −425.637 | −0.569033 | ||||||||
\(749\) | 421.291 | 0.562472 | ||||||||
\(750\) | 27.3861i | 0.0365148i | ||||||||
\(751\) | − | 650.518i | − | 0.866202i | −0.901345 | − | 0.433101i | \(-0.857419\pi\) | ||
0.901345 | − | 0.433101i | \(-0.142581\pi\) | |||||||
\(752\) | 208.927 | 0.277829 | ||||||||
\(753\) | − | 360.331i | − | 0.478528i | ||||||
\(754\) | −49.1118 | −0.0651350 | ||||||||
\(755\) | − | 333.476i | − | 0.441690i | ||||||
\(756\) | 118.684i | 0.156989i | ||||||||
\(757\) | − | 372.692i | − | 0.492328i | −0.969228 | − | 0.246164i | \(-0.920830\pi\) | ||
0.969228 | − | 0.246164i | \(-0.0791702\pi\) | |||||||
\(758\) | 493.234i | 0.650704i | ||||||||
\(759\) | 229.407 | − | 502.768i | 0.302249 | − | 0.662409i | ||||
\(760\) | −15.9974 | −0.0210493 | ||||||||
\(761\) | −127.577 | −0.167644 | −0.0838219 | − | 0.996481i | \(-0.526713\pi\) | ||||
−0.0838219 | + | 0.996481i | \(0.526713\pi\) | |||||||
\(762\) | −320.040 | −0.419999 | ||||||||
\(763\) | 1018.56 | 1.33494 | ||||||||
\(764\) | − | 209.362i | − | 0.274034i | ||||||
\(765\) | 102.912 | 0.134526 | ||||||||
\(766\) | 950.648i | 1.24106i | ||||||||
\(767\) | −243.822 | −0.317890 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | − | 1274.35i | − | 1.65715i | −0.559878 | − | 0.828575i | \(-0.689152\pi\) | ||
0.559878 | − | 0.828575i | \(-0.310848\pi\) | |||||||
\(770\) | 500.989i | 0.650635i | ||||||||
\(771\) | −802.117 | −1.04036 | ||||||||
\(772\) | 116.005 | 0.150266 | ||||||||
\(773\) | − | 1009.21i | − | 1.30557i | −0.757543 | − | 0.652785i | \(-0.773601\pi\) | ||
0.757543 | − | 0.652785i | \(-0.226399\pi\) | |||||||
\(774\) | − | 84.7333i | − | 0.109475i | ||||||
\(775\) | −13.5604 | −0.0174972 | ||||||||
\(776\) | − | 107.457i | − | 0.138476i | ||||||
\(777\) | −628.444 | −0.808808 | ||||||||
\(778\) | 657.074i | 0.844569i | ||||||||
\(779\) | − | 91.8751i | − | 0.117940i | ||||||
\(780\) | 23.1432i | 0.0296707i | ||||||||
\(781\) | 1395.39i | 1.78667i | ||||||||
\(782\) | 207.145 | − | 453.977i | 0.264891 | − | 0.580534i | ||||
\(783\) | 60.3956 | 0.0771336 | ||||||||
\(784\) | −325.697 | −0.415430 | ||||||||
\(785\) | −510.243 | −0.649992 | ||||||||
\(786\) | 7.31874 | 0.00931138 | ||||||||
\(787\) | − | 618.658i | − | 0.786096i | −0.919518 | − | 0.393048i | \(-0.871421\pi\) | ||
0.919518 | − | 0.393048i | \(-0.128579\pi\) | |||||||
\(788\) | 192.150 | 0.243845 | ||||||||
\(789\) | − | 58.8922i | − | 0.0746416i | ||||||
\(790\) | −191.791 | −0.242773 | ||||||||
\(791\) | −453.545 | −0.573382 | ||||||||
\(792\) | 117.710i | 0.148624i | ||||||||
\(793\) | − | 126.125i | − | 0.159047i | ||||||
\(794\) | −2.72053 | −0.00342636 | ||||||||
\(795\) | −230.424 | −0.289841 | ||||||||
\(796\) | − | 396.989i | − | 0.498729i | ||||||
\(797\) | − | 849.216i | − | 1.06552i | −0.846268 | − | 0.532758i | \(-0.821156\pi\) | ||
0.846268 | − | 0.532758i | \(-0.178844\pi\) | |||||||
\(798\) | 70.7580 | 0.0886692 | ||||||||
\(799\) | 801.301i | 1.00288i | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | 318.735i | 0.397921i | ||||||||
\(802\) | 590.125i | 0.735817i | ||||||||
\(803\) | − | 232.492i | − | 0.289530i | ||||||
\(804\) | − | 202.698i | − | 0.252112i | ||||||
\(805\) | −534.346 | − | 243.816i | −0.663784 | − | 0.302877i | ||||
\(806\) | −11.4594 | −0.0142177 | ||||||||
\(807\) | 865.875 | 1.07296 | ||||||||
\(808\) | −417.093 | −0.516205 | ||||||||
\(809\) | 194.891 | 0.240904 | 0.120452 | − | 0.992719i | \(-0.461566\pi\) | ||||
0.120452 | + | 0.992719i | \(0.461566\pi\) | |||||||
\(810\) | − | 28.4605i | − | 0.0351364i | ||||||
\(811\) | −224.475 | −0.276788 | −0.138394 | − | 0.990377i | \(-0.544194\pi\) | ||||
−0.138394 | + | 0.990377i | \(0.544194\pi\) | |||||||
\(812\) | 265.480i | 0.326946i | ||||||||
\(813\) | 427.238 | 0.525508 | ||||||||
\(814\) | −623.291 | −0.765713 | ||||||||
\(815\) | − | 582.577i | − | 0.714818i | ||||||
\(816\) | 106.287i | 0.130254i | ||||||||
\(817\) | −50.5171 | −0.0618324 | ||||||||
\(818\) | −1149.50 | −1.40526 | ||||||||
\(819\) | − | 102.364i | − | 0.124987i | ||||||
\(820\) | − | 162.440i | − | 0.198097i | ||||||
\(821\) | −472.157 | −0.575100 | −0.287550 | − | 0.957766i | \(-0.592841\pi\) | ||||
−0.287550 | + | 0.957766i | \(0.592841\pi\) | |||||||
\(822\) | 294.373i | 0.358118i | ||||||||
\(823\) | 1081.17 | 1.31370 | 0.656849 | − | 0.754022i | \(-0.271889\pi\) | ||||
0.656849 | + | 0.754022i | \(0.271889\pi\) | |||||||
\(824\) | − | 211.567i | − | 0.256756i | ||||||
\(825\) | − | 120.138i | − | 0.145621i | ||||||
\(826\) | 1318.01i | 1.59565i | ||||||||
\(827\) | − | 64.5413i | − | 0.0780427i | −0.999238 | − | 0.0390214i | \(-0.987576\pi\) | ||
0.999238 | − | 0.0390214i | \(-0.0124240\pi\) | |||||||
\(828\) | −125.548 | − | 57.2861i | −0.151628 | − | 0.0691861i | ||||
\(829\) | −548.619 | −0.661784 | −0.330892 | − | 0.943669i | \(-0.607350\pi\) | ||||
−0.330892 | + | 0.943669i | \(0.607350\pi\) | |||||||
\(830\) | −139.624 | −0.168222 | ||||||||
\(831\) | −607.674 | −0.731256 | ||||||||
\(832\) | −23.9022 | −0.0287286 | ||||||||
\(833\) | − | 1249.15i | − | 1.49958i | ||||||
\(834\) | −311.752 | −0.373803 | ||||||||
\(835\) | 396.031i | 0.474289i | ||||||||
\(836\) | 70.1777 | 0.0839447 | ||||||||
\(837\) | 14.0923 | 0.0168367 | ||||||||
\(838\) | − | 379.229i | − | 0.452540i | ||||||
\(839\) | − | 927.859i | − | 1.10591i | −0.833211 | − | 0.552955i | \(-0.813500\pi\) | ||
0.833211 | − | 0.552955i | \(-0.186500\pi\) | |||||||
\(840\) | 125.104 | 0.148933 | ||||||||
\(841\) | −705.903 | −0.839361 | ||||||||
\(842\) | 246.211i | 0.292412i | ||||||||
\(843\) | 402.489i | 0.477448i | ||||||||
\(844\) | −308.147 | −0.365103 | ||||||||
\(845\) | 357.935i | 0.423591i | ||||||||
\(846\) | 221.601 | 0.261939 | ||||||||
\(847\) | − | 815.880i | − | 0.963259i | ||||||
\(848\) | − | 237.981i | − | 0.280638i | ||||||
\(849\) | − | 801.570i | − | 0.944135i | ||||||
\(850\) | − | 108.479i | − | 0.127622i | ||||||
\(851\) | 303.337 | − | 664.791i | 0.356447 | − | 0.781189i | ||||
\(852\) | 348.448 | 0.408976 | ||||||||
\(853\) | −348.485 | −0.408540 | −0.204270 | − | 0.978915i | \(-0.565482\pi\) | ||||
−0.204270 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(854\) | −681.783 | −0.798341 | ||||||||
\(855\) | −16.9679 | −0.0198454 | ||||||||
\(856\) | − | 104.339i | − | 0.121892i | ||||||
\(857\) | 1026.47 | 1.19774 | 0.598872 | − | 0.800845i | \(-0.295616\pi\) | ||||
0.598872 | + | 0.800845i | \(0.295616\pi\) | |||||||
\(858\) | − | 101.525i | − | 0.118327i | ||||||
\(859\) | 1188.51 | 1.38360 | 0.691801 | − | 0.722088i | \(-0.256817\pi\) | ||||
0.691801 | + | 0.722088i | \(0.256817\pi\) | |||||||
\(860\) | −89.3167 | −0.103857 | ||||||||
\(861\) | 718.484i | 0.834476i | ||||||||
\(862\) | − | 412.897i | − | 0.478999i | ||||||
\(863\) | −1055.95 | −1.22359 | −0.611793 | − | 0.791018i | \(-0.709551\pi\) | ||||
−0.611793 | + | 0.791018i | \(0.709551\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | − | 17.0142i | − | 0.0196696i | ||||||
\(866\) | 620.996i | 0.717086i | ||||||||
\(867\) | 92.9180 | 0.107172 | ||||||||
\(868\) | 61.9456i | 0.0713659i | ||||||||
\(869\) | 841.348 | 0.968180 | ||||||||
\(870\) | − | 63.6625i | − | 0.0731753i | ||||||
\(871\) | 174.826i | 0.200719i | ||||||||
\(872\) | − | 252.263i | − | 0.289292i | ||||||
\(873\) | − | 113.975i | − | 0.130556i | ||||||
\(874\) | −34.1534 | + | 74.8504i | −0.0390771 | + | 0.0856412i | ||||
\(875\) | −127.683 | −0.145924 | ||||||||
\(876\) | −58.0565 | −0.0662745 | ||||||||
\(877\) | −921.525 | −1.05077 | −0.525385 | − | 0.850865i | \(-0.676079\pi\) | ||||
−0.525385 | + | 0.850865i | \(0.676079\pi\) | |||||||
\(878\) | −87.7724 | −0.0999685 | ||||||||
\(879\) | 283.685i | 0.322736i | ||||||||
\(880\) | 124.078 | 0.140997 | ||||||||
\(881\) | − | 1210.60i | − | 1.37412i | −0.726600 | − | 0.687061i | \(-0.758901\pi\) | ||
0.726600 | − | 0.687061i | \(-0.241099\pi\) | |||||||
\(882\) | −345.454 | −0.391671 | ||||||||
\(883\) | −386.146 | −0.437311 | −0.218656 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218656 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(884\) | − | 91.6722i | − | 0.103702i | ||||||
\(885\) | − | 316.061i | − | 0.357131i | ||||||
\(886\) | −369.697 | −0.417265 | ||||||||
\(887\) | −493.959 | −0.556887 | −0.278444 | − | 0.960453i | \(-0.589819\pi\) | ||||
−0.278444 | + | 0.960453i | \(0.589819\pi\) | |||||||
\(888\) | 155.644i | 0.175275i | ||||||||
\(889\) | − | 1492.13i | − | 1.67844i | ||||||
\(890\) | 335.976 | 0.377501 | ||||||||
\(891\) | 124.851i | 0.140124i | ||||||||
\(892\) | −176.542 | −0.197916 | ||||||||
\(893\) | − | 132.116i | − | 0.147946i | ||||||
\(894\) | 322.452i | 0.360685i | ||||||||
\(895\) | − | 714.164i | − | 0.797948i | ||||||
\(896\) | 129.206i | 0.144204i | ||||||||
\(897\) | 108.285 | + | 49.4090i | 0.120719 | + | 0.0550825i | ||||
\(898\) | 609.985 | 0.679271 | ||||||||
\(899\) | 31.5228 | 0.0350643 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 912.730 | 1.01302 | ||||||||
\(902\) | 712.592i | 0.790013i | ||||||||
\(903\) | 395.055 | 0.437492 | ||||||||
\(904\) | 112.328i | 0.124256i | ||||||||
\(905\) | −257.508 | −0.284539 | ||||||||
\(906\) | 365.305 | 0.403206 | ||||||||
\(907\) | 332.986i | 0.367129i | 0.983008 | + | 0.183565i | \(0.0587637\pi\) | ||||
−0.983008 | + | 0.183565i | \(0.941236\pi\) | |||||||
\(908\) | 440.991i | 0.485673i | ||||||||
\(909\) | −442.394 | −0.486682 | ||||||||
\(910\) | −107.901 | −0.118573 | ||||||||
\(911\) | − | 310.817i | − | 0.341182i | −0.985342 | − | 0.170591i | \(-0.945432\pi\) | ||
0.985342 | − | 0.170591i | \(-0.0545677\pi\) | |||||||
\(912\) | − | 17.5243i | − | 0.0192153i | ||||||
\(913\) | 612.504 | 0.670870 | ||||||||
\(914\) | 1038.84i | 1.13659i | ||||||||
\(915\) | 163.493 | 0.178680 | ||||||||
\(916\) | 276.227i | 0.301557i | ||||||||
\(917\) | 34.1225i | 0.0372110i | ||||||||
\(918\) | 112.735i | 0.122805i | ||||||||
\(919\) | 487.215i | 0.530158i | 0.964227 | + | 0.265079i | \(0.0853980\pi\) | ||||
−0.964227 | + | 0.265079i | \(0.914602\pi\) | |||||||
\(920\) | −60.3848 | + | 132.339i | −0.0656357 | + | 0.143847i | ||||
\(921\) | −622.941 | −0.676375 | ||||||||
\(922\) | 885.327 | 0.960225 | ||||||||
\(923\) | −300.534 | −0.325606 | ||||||||
\(924\) | −548.806 | −0.593946 | ||||||||
\(925\) | − | 158.854i | − | 0.171734i | ||||||
\(926\) | −453.574 | −0.489821 | ||||||||
\(927\) | − | 224.401i | − | 0.242072i | ||||||
\(928\) | 65.7504 | 0.0708517 | ||||||||
\(929\) | 1224.58 | 1.31817 | 0.659085 | − | 0.752068i | \(-0.270944\pi\) | ||||
0.659085 | + | 0.752068i | \(0.270944\pi\) | |||||||
\(930\) | − | 14.8546i | − | 0.0159727i | ||||||
\(931\) | 205.956i | 0.221220i | ||||||||
\(932\) | 196.375 | 0.210703 | ||||||||
\(933\) | 544.882 | 0.584011 | ||||||||
\(934\) | 209.892i | 0.224724i | ||||||||
\(935\) | 475.877i | 0.508959i | ||||||||
\(936\) | −25.3521 | −0.0270856 | ||||||||
\(937\) | 412.886i | 0.440647i | 0.975427 | + | 0.220323i | \(0.0707112\pi\) | ||||
−0.975427 | + | 0.220323i | \(0.929289\pi\) | |||||||
\(938\) | 945.047 | 1.00751 | ||||||||
\(939\) | − | 782.418i | − | 0.833246i | ||||||
\(940\) | − | 233.588i | − | 0.248498i | ||||||
\(941\) | 729.608i | 0.775354i | 0.921795 | + | 0.387677i | \(0.126722\pi\) | ||||
−0.921795 | + | 0.387677i | \(0.873278\pi\) | |||||||
\(942\) | − | 558.944i | − | 0.593359i | ||||||
\(943\) | −760.038 | − | 346.797i | −0.805979 | − | 0.367759i | ||||
\(944\) | 326.426 | 0.345790 | ||||||||
\(945\) | 132.692 | 0.140415 | ||||||||
\(946\) | 391.815 | 0.414181 | ||||||||
\(947\) | 1691.14 | 1.78579 | 0.892894 | − | 0.450268i | \(-0.148671\pi\) | ||||
0.892894 | + | 0.450268i | \(0.148671\pi\) | |||||||
\(948\) | − | 210.096i | − | 0.221620i | ||||||
\(949\) | 50.0734 | 0.0527644 | ||||||||
\(950\) | 17.8857i | 0.0188270i | ||||||||
\(951\) | 310.128 | 0.326107 | ||||||||
\(952\) | −495.547 | −0.520532 | ||||||||
\(953\) | − | 133.087i | − | 0.139651i | −0.997559 | − | 0.0698255i | \(-0.977756\pi\) | ||
0.997559 | − | 0.0698255i | \(-0.0222443\pi\) | |||||||
\(954\) | − | 252.417i | − | 0.264588i | ||||||
\(955\) | −234.074 | −0.245104 | ||||||||
\(956\) | −842.438 | −0.881211 | ||||||||
\(957\) | 279.275i | 0.291824i | ||||||||
\(958\) | − | 1059.49i | − | 1.10594i | ||||||
\(959\) | −1372.47 | −1.43114 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | −953.645 | −0.992346 | ||||||||
\(962\) | − | 134.242i | − | 0.139545i | ||||||
\(963\) | − | 110.669i | − | 0.114921i | ||||||
\(964\) | − | 363.505i | − | 0.377080i | ||||||
\(965\) | − | 129.698i | − | 0.134402i | ||||||
\(966\) | 267.087 | − | 585.347i | 0.276488 | − | 0.605949i | ||||
\(967\) | 310.427 | 0.321020 | 0.160510 | − | 0.987034i | \(-0.448686\pi\) | ||||
0.160510 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(968\) | −202.065 | −0.208745 | ||||||||
\(969\) | 67.2112 | 0.0693614 | ||||||||
\(970\) | −120.141 | −0.123856 | ||||||||
\(971\) | − | 1571.54i | − | 1.61847i | −0.587483 | − | 0.809237i | \(-0.699881\pi\) | ||
0.587483 | − | 0.809237i | \(-0.300119\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | − | 1453.49i | − | 1.49383i | ||||||
\(974\) | 408.880 | 0.419794 | ||||||||
\(975\) | 25.8749 | 0.0265383 | ||||||||
\(976\) | 168.854i | 0.173006i | ||||||||
\(977\) | − | 283.092i | − | 0.289757i | −0.989449 | − | 0.144878i | \(-0.953721\pi\) | ||
0.989449 | − | 0.144878i | \(-0.0462791\pi\) | |||||||
\(978\) | 638.181 | 0.652537 | ||||||||
\(979\) | −1473.86 | −1.50548 | ||||||||
\(980\) | 364.141i | 0.371572i | ||||||||
\(981\) | − | 267.565i | − | 0.272747i | ||||||
\(982\) | 1087.25 | 1.10718 | ||||||||
\(983\) | − | 1310.77i | − | 1.33344i | −0.745310 | − | 0.666718i | \(-0.767698\pi\) | ||
0.745310 | − | 0.666718i | \(-0.232302\pi\) | |||||||
\(984\) | 177.944 | 0.180837 | ||||||||
\(985\) | − | 214.830i | − | 0.218101i | ||||||
\(986\) | 252.173i | 0.255754i | ||||||||
\(987\) | 1033.18i | 1.04679i | ||||||||
\(988\) | 15.1146i | 0.0152982i | ||||||||
\(989\) | −190.685 | + | 417.904i | −0.192806 | + | 0.422552i | ||||
\(990\) | 131.604 | 0.132934 | ||||||||
\(991\) | −999.520 | −1.00860 | −0.504299 | − | 0.863529i | \(-0.668249\pi\) | ||||
−0.504299 | + | 0.863529i | \(0.668249\pi\) | |||||||
\(992\) | 15.3418 | 0.0154655 | ||||||||
\(993\) | 915.905 | 0.922361 | ||||||||
\(994\) | 1624.58i | 1.63439i | ||||||||
\(995\) | −443.847 | −0.446077 | ||||||||
\(996\) | − | 152.950i | − | 0.153565i | ||||||
\(997\) | −806.118 | −0.808543 | −0.404272 | − | 0.914639i | \(-0.632475\pi\) | ||||
−0.404272 | + | 0.914639i | \(0.632475\pi\) | |||||||
\(998\) | 285.086 | 0.285657 | ||||||||
\(999\) | 165.085i | 0.165251i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.3.c.a.91.28 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.16 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.29 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.28 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.29 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.1 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.16 | 32 | 3.2 | odd | 2 |